Answer:
Correct choice: C. [tex]x=\pm\sqrt{10}\mathbf{i}[/tex]
Step-by-step explanation:
The quadratic equation to solve is:
[tex]x^2+10=0[/tex]
Since this equation is incomplete, we can solve it without using the quadratic solver formula.
Subtracting 10:
[tex]x^2=-10[/tex]
Taking square root:
[tex]x=\pm\sqrt{-10}[/tex]
Recall the square root of a negative number leads to imaginary solutions where the Unit Imaginary Number (i) is used, where:
[tex]\mathbf{i}=\sqrt{-1}[/tex]
The solutions to the equation are:
[tex]x=\pm\sqrt{10}\mathbf{i}[/tex]
Correct choice: C. [tex]x=\pm\sqrt{10}\mathbf{i}[/tex]
